Match the following based on the construction of similar triangles, if scale factor ( $\frac{m}{n}$ ) is

I. >1

II. <1

III. =1

a) The similar triangle is smaller than the original triangle.

b) The two triangles are congruent triangles.

c) The similar triangle is larger than the original triangle.

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Solution

Scale factor basically defines the ratio between the sides of the constructed triangle to that of the original triangle. So when we see the scale factor is greater than 1, it means the sides of the constructed triangle is larger than the original triangle i.e. the triangle constructed is larger than the original triangle.

Similarly, if scale factor $\frac{m}{n}$ is smaller than 1 then the sides of the constructed triangle is smaller than that of the original triangle i.e. the constructed triangle is smaller than the original triangle.

And when we have scale factor equal to 1, then the sides of both the constructed triangle and that of the original triangle is equal. When a pair of similar triangles have their equal corresponding sides, then the pair of similar triangles can be called as congruent because the triangle have equal corresponding sides and equal corresponding angles.

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Match the following based on the construction of similar triangles, if scale factor (mn) is I. >1 II. <1 III. =1 a) The similar triangle is smaller than the original triangle. b) The two triangles are congruent triangles. c) The similar triangle is larger than the original triangle.